Syz mirror symmetry for toric calabi-yau manifolds

Kwokwai Chan The Chinese University of Hong Kong Siu-Cheong Lau Mathematics of the Universe Naichung Conan Leung The Chinese University of Hong Kong

Differential Geometry mathscidoc:1609.10250

Journal of Differential Geometry, 90, (1), 177-250, 2012
In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that generalizes the standard notion of open book decomposition and allows one to more easily study surgeries on transverse knots. As a corollary to our investigation we are able to show there are Stein fillable contact structures supported by open books whose monodromies cannot be written as a product of positive Dehn twists. We also exhibit several monoids in the mapping class group of a surface that have contact geometric significance.
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@inproceedings{kwokwai2012syz,
  title={SYZ MIRROR SYMMETRY FOR TORIC CALABI-YAU MANIFOLDS},
  author={Kwokwai Chan, Siu-Cheong Lau, and Naichung Conan Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223313891841912},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={1},
  pages={177-250},
  year={2012},
}
Kwokwai Chan, Siu-Cheong Lau, and Naichung Conan Leung. SYZ MIRROR SYMMETRY FOR TORIC CALABI-YAU MANIFOLDS. 2012. Vol. 90. In Journal of Differential Geometry. pp.177-250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223313891841912.
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